Answer:
The equation of the line is y = [tex]-\frac{5}{6}[/tex] x - 2
Step-by-step explanation:
The form of the linear function is y = m x + b, where
The rule of the slope is m =[tex]\frac{y2-y1}{x2-x1}[/tex] , where
- (x1, y1) and (x2, y2) are two points on the line
∵ The line passes through points (6, -7) and (-6, 3)
∴ x1 = 6 and y1 = -7
∴ x2 = -6 and y2 = 3
→ Substitute them in the rule of the slope above to find it
∵ m = [tex]\frac{3--7}{-6-6}[/tex] = [tex]\frac{3+7}{-12}[/tex] = [tex]\frac{10}{-12}[/tex] = [tex]\frac{5}{-6}[/tex]
∴ m = [tex]-\frac{5}{6}[/tex]
→ Substitute it in the form of the equation above
∴ y = [tex]-\frac{5}{6}[/tex] x + b
→ Substitute x and y in the equation by x1 and y1
∵ x1 = 6 and y1 = -7
∴ -7 = [tex]-\frac{5}{6}[/tex] (6) + b
∴ -7 = -5 + b
→ Add 5 to both sides
∵ -7 + 5 = -5 + 5 + b
∴ -2 = b
→ Substitute the value of b in the equation
∴ y = [tex]-\frac{5}{6}[/tex] x + -2
∴ y = [tex]-\frac{5}{6}[/tex] x - 2
∴ The equation of the line is y = [tex]-\frac{5}{6}[/tex] x - 2
